Falsifiability

In common language, a statement is falsifiable (or disprovable) if some observation might contradict it. In the philosophy of science, it is the same, except that the observations used to show falsifiability (or refutability) are logical constructions that can be impossible.[upper-alpha 1] For example, the law "All swans are white" is falsifiable because "Here is a black swan" contradicts it and, even if it was impossible, it would still contradict it and make the law falsifiable.[upper-alpha 2]

The observation of these black swans contradicts the law "All swans are white", but even if there were no black swans, the law would still be falsifiable, because identifying a swan and observing the color black would remain possible.

Likewise, the law "All ravens are black" is falsifiable, although it is still held to be true. Observing e.g. a red raven could show it to be false. In contrast, the sentence "Some time, a red raven will appear" is not falsifiable since it is too unspecific to admit a contradicting observation.

Falsifiability was introduced by the philosopher of science Karl Popper in his book Logik der Forschung (1934, revised and translated into English in 1959 as The Logic of Scientific Discovery), as an attempt to solve both the problem of induction and the demarcation problem. He saw falsifiability as the cornerstone of critical rationalism, his theory of science.[1]

Popper opposed falsifiability to verifiability. For example, in order to verify the claim "All swans are white" one would have to observe every swan, which is not possible, whereas the single observation "Here is a black swan" is sufficient to falsify it.

As a key notion in the separation of science from non-science, falsifiability has featured prominently in many scientific controversies and applications, even being used as legal precedent.

Falsificationism: a solution to the problem of induction

One of the questions in scientific method is: how does one move from observations to scientific laws? This is the problem of induction. Suppose we want to put the theory that all swans are white to the test. We come across a white swan. We cannot validly argue from "here is a white swan" to "all swans are white"; doing so would require a fallacious logic such as, for example, affirming the consequent.[upper-alpha 3][2]

Popper's basic idea to solve this problem is to flip it upside down. He noticed that while it is impossible to verify that every swan is white, finding a single black swan shows that not every swan is white. We might tentatively accept the proposal that every swan is white, while looking out for examples of non-white swans that would show our conjecture to be false. This is the basis of critical rationalism.

Falsification uses the valid inference modus tollens: if from a statement $P$ (say some law with some initial condition) we logically deduce $Q$ , but what is observed is $\neg Q$ , we infer that $P$ is false. For example, given the law "all swans are white" and the initial condition "there is a swan here", we can deduce "the swan here is white", but if what is observed is "the swan here is not white" (say black), then "all swans are white" is false, or it was not a swan.[upper-alpha 4]

Popper was aware that this basic idea would be subject to valid criticisms. Imre Lakatos, realizing that Popper's critical rationalism was misunderstood, defined "sophisticated falsificationism" and contrasted it with weaker versions of falsificationism, which he called dogmatic falsificationism and naive falsificationism.[3] Popper's solution is not (and never has been) one of these two weak versions[upper-alpha 5] and to address the intricacies of section § The demarcation problem it has to be more than sophisticated falsificationism. Also, on the terminological side of this issue, Popper never used the term "falsificationism"[upper-alpha 6] and proposed instead the term "critical rationalism".[upper-alpha 7]

Away from dogmatic falsificationism

A dogmatic falsificationist ignores that every observation is theory impregnated. This leads to the critique that it is unclear which theory is falsified. Is it the one that is being studied or the one behind the observation?[upper-alpha 8] This is sometimes called the 'Duhem–Quine problem'. An example is Galileo's refutation of the time-honoured theory that celestial bodies are faultless crystal balls. Many considered that it was the optical theory of the telescope that was false, not the theory of celestial bodies. A dogmatic falsificationist ignores a more subtle fact: only statements can contradict statements. So, it is fundamentally incorrect to say that an observation contradicts a theory.

A dogmatic falsificationist further ignores the role of auxiliary hypotheses, which could explain the contradicting observation. For the falsification to logically occur, a ceteris paribus clause must say that no auxiliary hypothesis is responsible for the contradicting observation. Again, this leads to the critique that it cannot be told if it is the theory or the ceteris paribus clause that is false. Lakatos gives the example of the path of a planet. If the path contradicts Newton's law, we will not know if it is Newton's law that is false or the assumption that no other body influenced the path. Popper was aware that one can always find another auxiliary hypothesis,[upper-alpha 9] though he clearly distinguished falsifiable theories such as Newton theory and non falsifiable theories on this respect.[upper-alpha 10]

Lakatos explains that Popper's solution to these valid criticisms against dogmatic falsificationism requires that one relaxes the dogmatic assumption that an observation can show a theory to be false[upper-alpha 11]:

If a theory is falsified [in the usual sense], it is proven false; if it is falsified [in the technical sense], it may still be true.
— Imre Lakatos, Lakatos 1978, p. 24

Methodological falsificationism replaces the contradicting observation in a falsification with a "contradicting observation" accepted by convention among scientists, a convention that implies three decisions: the theory underlying the observation is correct, no auxiliary hypotheses explain this observation and the written form of the observation matches with an actual observation.[upper-alpha 12] The falsifiers thus depend on decisions made by scientists in view of the currently accepted technology and its associated theory. So, Popper says that "Science does not rest upon solid bedrock".[upper-alpha 13] He also says (see section § Basic statements and the definition of falsifiability) that it's not an obstacle to the definition of an empirical basis and of falsifiability.

Away from naive falsificationism

Naive falsificationism is the claim that methodological falsifications can by themselves explain how scientific knowledge progresses. Very often one must deal with two or more competing theories which can both be non-falsified (say by not making the proper decisions). Considering only falsifications, it is not clear why one theory is chosen above the other. It is not clear why often a corroborating experiment is seen as a sign of progress. Popper's falsificationism or critical rationalism uses both falsifications and corroborations to explain progress in science.[upper-alpha 14] How corroborations and falsifications can explain progress in science was a subject of disagreement between many philosophers, especially between Lakatos and Popper.[upper-alpha 15]

Popper clearly distinguished between the creative and informal process from which theories emerge and the logical and formal process where theories are falsified or corroborated.[upper-alpha 16][upper-alpha 17][upper-alpha 18] The main issue is whether the decision to select a theory among competing theories in the light of falsifications and corroborations should be moved in the logical part as some kind of formal logic.[upper-alpha 19] It is a delicate question, because this logic could be considered as inductive: it selects a universal law in view of instances. The answer of Lakatos and many others to that question is that it should.[upper-alpha 20][upper-alpha 21] In contradistinction, for Popper, the creative and informal part is guided by methodological rules, which naturally say to favor theories that are corroborated[upper-alpha 22], but this methodology can hardly be made rigorous.[upper-alpha 23] Popper does not mention corroborations when he describes the purely logical part.[upper-alpha 24]

Popper's way to analyze progress in science was through the concept of verisimilitude, a way to define how close a theory is to the truth, which he did not consider very significant, except (as an attempt) to clarify a concept already clear in practice. Later, it was shown that the specific definition proposed by Popper cannot distinguish between two theories that are false, which is the case for all theories in the history of science.[upper-alpha 25] Today, there is still on going research on the general concept of verisimilitude.[4]

The demarcation problem

Popper's response to the problem of induction is simply that induction is actually never used in science.[upper-alpha 26] Instead, laws are conjectured, tested and the results are considered together with other aspects to decide which of these laws are applied in practice.[5] In contradistinction, the logical empiricism movement, which included such philosophers as Moritz Schlick, Rudolf Carnap, Otto Neurath and A.J. Ayer wanted to formalize the idea that, for a law to be scientific, it must be possible to argue on the basis of observations either in favor of its truth or its falsity. There was no consensus among these philosophers about how to achieve that, but the thought expressed by Mach's dictum that "where neither confirmation nor refutation is possible, science is not concerned" was accepted as a basic precept of critical reflection about science.[6][7] In this logical positivism perspective, Popper's suggestion that we can only argue for the falsity of laws can be interpreted as if only falsifications, no confirmations, are possible in science. But, a criterion that accepts only laws that can be argued to be false is not useful.

Popper explained that a demarcation criterion was still possible, but we have to use the logical possibility of "falsifications", not falsifications as such. He pointed out his encounter with psychoanalysis in the years 1910. It did not matter what observation was presented, psychoanalysis could explain it. Unfortunately, the reason why it could explain everything is that it did not exclude anything also.[upper-alpha 27] For Popper, this was a failure, because it meant that it could not make any prediction. From a logical standpoint, if one finds an observation that does not contradict a law, it does not mean that the law is true. A verification has no value in itself. But, if the law makes risky predictions and these are corroborated, Popper says, there is a reason to prefer this law over another law that makes less risky predictions or no predictions at all. In the definition of falsifiability, contradictions with observations are not used for actual falsifications, but for logical "falsifications" that show that the law makes risky predictions, which is completely different.

On the basic philosophical side of this issue, Popper argued that some philosophers of the Vienna Circle had mixed two different problems, that of meaning and that of demarcation, and had proposed in verificationism a single solution to both: a statement that could not be verified was considered meaningless. In opposition to this view, Popper emphasized that there are meaningful theories that are not scientific, and that, accordingly, a criterion of meaningfulness does not coincide with a criterion of demarcation.

Basic statements and the definition of falsifiability

Popper always made a clear distinction between the logic of science and its applied methodology.[upper-alpha 16] The logical part consists of theories, statements and their purely logical relationship. The methodological part consists, in Popper's view, of informal rules, which are used to guess theories, accept observation statements as factual, etc. When this distinction is applied to the term "falsifiability", it corresponds to a distinction between two completely different meanings of the term. The same is true for the term "falsifiable". Popper explained that he only uses "falsifiability" or "falsifiable" in reference to the logical side and that, when he refers to the methodological side, he speaks instead of "falsification" and its problems.[upper-alpha 11]

Popper said that methodological problems require proposing methodological rules. For example, one such rule is that, if one refuses to go along with falsifications, then one has retired oneself from the game of science. The logical side does not have such methodological problems, in particular with regard to the falsifiability of a theory, because basic statements are not required to be possible. Methodological rules are only needed in the context of actual falsifications.

So observations have two purposes in Popper's view. On the methodological side, observations can be used to show that a law is false, which Popper calls falsification. On the logical side, observations, which are purely logical constructions, do not show a law to be false, but contradict a law to show its falsifiability. Unlike falsifications and free from the problems of falsifications, these contradictions establish the value of the law, which may eventually be corroborated. He wrote that an entire literature exists because this distinction was not understood.[upper-alpha 1]

Basic statements

In Popper's view of science, statements of observation can be constructed within a logical structure independently of any factual observations.[upper-alpha 28][8] The set of all purely logical observations that can be created constitutes the empirical "basis". Popper calls them the basic statements or test statements. They are the statements that can be used to show the falsifiability of a theory. Popper insists that a basic statement does not have to be possible in practice. It is sufficient that the values or properties that appear in the observations are associated with technologies.

Even if it is accepted that angels exist, the sentence "All angels have large wings" is not falsifiable, because though it is possible to observe the absence of large wings, no technology (independent of the presence of wings) exists to identify these angels.

Popper gives the example of an apple that moves from the ground up to a branch and then starts to dance from one branch to another.[upper-alpha 29] It is clearly impossible, yet a valid potential falsifier for Newton's theory, because the position of the apple at different times can be measured. In contrast, "this man is immortal" is not a basic statement, because no technology can decide that a man is immortal. Indeed, "All men are mortal" is a classical example of an unfalsifiable statement. Another example is "this angel does not have large wings". It is not a basic statement, because though the absence of large wings can be observed, no technology (independent of the presence of wings[upper-alpha 30]) exists to identify angels.

In more than twelve pages of The Logic of Scientific Discovery (Popper 1959, sec. 13–15, 28), Popper discusses informally which statements among those that can be constructed in the logical structure are basic statements. A logical structure uses universal classes to define laws. For example, in the law "all swans are white" the concept of swans is a universal class. It corresponds to a set of properties that every swan must have. It is not restricted to the swans that exist, existed or will exist. Informally, a basic statement is simply a statement that concerns only a finite number of specific instances in universal classes. In particular, an existential statement such as "there exists a black swan" is not a basic statement, because it is not specific about the instance. On the other hand, "this swan here is black" is a basic statement. Popper says that it is a singular existential statement or simply a singular statement. So, basic statements are singular (existential) statements.

The definition of falsifiability: beyond sophisticated falsificationism

Thornton says that basic statements are statements that correspond to particular "observation-reports". He then gives Popper's definition of falsifiability:

"A theory is scientific if and only if it divides the class of basic statements into the following two non-empty sub-classes: (a) the class of all those basic statements with which it is inconsistent, or which it prohibits—this is the class of its potential falsifiers (i.e., those statements which, if true, falsify the whole theory), and (b) the class of those basic statements with which it is consistent, or which it permits (i.e., those statements which, if true, corroborate it, or bear it out)."
— Thornton, Stephen, Thornton 2016, at the end of section 3

As in the case of actual falsifiers, decisions must be taken by scientists to accept a logical structure and its associated empirical basis, but these are usually part of a background knowledge that scientists have in common and, often, no discussion is even necessary.[upper-alpha 31] The first decision described by Lakatos is implicit in this agreement, but the other decisions are not needed. This agreement, if one can speak of agreement when there is not even a discussion, exists only in principle. This is where the distinction between the logical and methodological sides of science becomes important. When an actual falsifier is proposed, the technology used is considered in details and, as mentioned in section § Away from dogmatic falsificationism, an actual agreement is needed. This may require using a deeper empirical basis[upper-alpha 32], hidden within the current empirical basis, to make sure that the properties or values used in the falsifier were obtained correctly (Andersson 2016 gives some examples).

Despite the fact that the empirical basis can be shaky, more comparable to a swamp than to a solid ground, the definition that is given above is simply the formalization of a natural requirement on scientific theories, without which, Popper says, the whole logical process of science[upper-alpha 28] would not be possible.

Controversies

Kuhn

Thomas Kuhn emphasized aspects of science that were not much considered by Popper. In particular, he analyzed what he calls periods of normal science as well as revolutions from one period of normal science to another,[9] whereas Popper's view is that only revolutions are relevant.[upper-alpha 33][upper-alpha 34] For Popper, the role of science, mathematics and metaphysics, actually the role of any knowledge, is to solve puzzles.[upper-alpha 35] In the same line of thought, Kuhn observes that in periods of normal science the scientific theories, which represent some paradigm, are used to routinely solve puzzles and the validity of the paradigm is hardly in question. It's only when important new puzzles emerge that cannot be solved by accepted theories that a revolution might occur. This can be seen as a viewpoint on the distinction made by Popper between the informal and formal process in science (see section § Away from naive falsificationism). In the big picture presented by Kuhn, the routinely solved puzzles are corroborations. Falsifications or otherwise unexplained observations are unsolved puzzles. All of these are used in the informal process that generates a new kind of theory. Kuhn says that Popper emphasizes formal or logical falsifications and fails to explain how the social and informal process works.

Feyerabend

Paul Feyerabend examined the history of science with a more critical eye, and ultimately rejected any prescriptive methodology at all. He rejected Lakatos' argument for ad hoc hypothesis, arguing that science would not have progressed without making use of any and all available methods to support new theories. He rejected any reliance on a scientific method, along with any special authority for science that might derive from such a method.[10] Rather, he claimed that if one is keen to have a universally valid methodological rule, epistemological anarchism or anything goes would be the only candidate.[11] For Feyerabend, any special status that science might have derives from the social and physical value of the results of science rather than its method.[12]

Sokal and Bricmont

In their book Fashionable Nonsense (from 1997, published in the UK as Intellectual Impostures) the physicists Alan Sokal and Jean Bricmont criticised falsifiability.[13] They include this critique in the "Intermezzo" chapter, where they expose their own views on truth in contrast to the extreme epistemological relativism of postmodernism. Even though Popper is clearly not a relativist, Sokal and Bricmont discuss falsifiability because they see postmodernist epistemological relativism as a reaction to Popper's insistence on falsifiability, and more generally, to his theory of science.[14]

Applications

Use in courts of law

Falsifiability has been used in the McLean v. Arkansas case (in 1982),[15] the Daubert case (in 1993)[16] and other cases. A survey of 303 federal judges conducted in 1998 revealed that "[P]roblems with the nonfalsifiable nature of an expert's underlying theory and difficulties with an unknown or too-large error rate were cited in less than 2% of cases."[upper-alpha 36]

McLean v. Arkansas case

In the ruling of the McLean v. Arkansas case, Judge William Overton used falsifiability as one of the criteria to determine that "creation science" was not scientific and should not be taught in Arkansas public schools as such (it can be taught as religion). In his testimony, philosopher Michael Ruse defined the characteristics which constitute science as (see Pennock 2000, p. 5 and Ruse 2010):

It is guided by natural law;
It has to be explanatory by reference to natural law;
It is testable against the empirical world;
Its conclusions are tentative, i.e., are not necessarily the final word; and
It is falsifiable.

In his conclusion related to this criterion Judge Overton stated that

While anybody is free to approach a scientific inquiry in any fashion they choose, they cannot properly describe the methodology as scientific, if they start with the conclusion and refuse to change it regardless of the evidence developed during the course of the investigation.
— William Overton, McLean v. Arkansas 1982, at the end of section IV. (C)

Daubert v. Merrell Dow Pharmaceuticals case

In the Daubert case, the majority opinion proposed the so-called five Daubert factors, which include falsifiability, to define a scientific methodology that is acceptable in courts of law.[upper-alpha 37] These original Daubert factors have been cited in the Kumho Tire Co. v. Carmichael case and in the U.S. v. PRIME case (United States v. Prime 2002). In the Daubert case, Associate Justice Harry Blackmun, delivering the majority opinion of the United States Supreme Court, has cited Popper and other philosophers of science:

Ordinarily, a key question to be answered in determining whether a theory or technique is scientific knowledge that will assist the trier of fact will be whether it can be (and has been) tested. Scientific methodology today is based on generating hypotheses and testing them to see if they can be falsified; indeed, this methodology is what distinguishes science from other fields of human inquiry. Green 645. See also C. Hempel, Philosophy of Natural Science 49 (1966) ([T]he statements constituting a scientific explanation must be capable of empirical test); K. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge 37 (5th ed. 1989) ([T]he criterion of the scientific status of a theory is its falsifiability, or refutability, or testability) (emphasis deleted).
— Harry Blackmun, Daubert 1993, p. 593

In a partially dissident opinion, Chief Justice William Rehnquist supported by Associate Justice John Paul Stevens, responded that:

I defer to no one in my confidence in federal judges; but I am at a loss to know what is meant when it is said that the scientific status of a theory depends on its falsifiability, and I suspect some of them will be, too.
— William Rehnquist, Daubert 1993, p. 600

Professor of Law David H. Kaye[upper-alpha 38] argued that references to the Daubert majority opinion confused falsifiability and falsification and that "inquiring into the existence of meaningful attempts at falsification is an appropriate and crucial consideration in admissibility determinations."[upper-alpha 39]

Economics

Karl Popper argued that Marxism shifted from scientific to unscientific.[upper-alpha 40]

Some economists, such as those of the Austrian School, believe that macroeconomics is empirically unfalsifiable and that thus the only appropriate means to understand economic events is by logically studying the intentions of individual economic decision-makers, based on certain fundamental truths.[17][18] Prominent figures within the Austrian School of economics, Ludwig von Mises and Friedrich Hayek were associates of Karl Popper, with whom they co-founded the Mont Pelerin Society.

Evolution

Numerous examples of potential (indirect) ways to falsify common descent have been proposed by its proponents.[19] J.B.S. Haldane, when asked what hypothetical evidence could disprove evolution, replied "fossil rabbits in the Precambrian era".[20] Richard Dawkins adds that any other modern animal, such as a hippo, would suffice.[21][22][23] Karl Popper at first spoke against the testability of natural selection[24][25] but recanted, "I have changed my mind about the testability and logical status of the theory of natural selection, and I am glad to have the opportunity to make a recantation."[26]

Omphalos hypothesis

Much of the criticism against young-Earth creationism is based on evidence in nature that the Earth is much older than adherents believe. Confronting such evidence, some adherents make an argument (called the Omphalos hypothesis) that the world was created with the appearance of age; e.g., the sudden appearance of a mature chicken capable of laying eggs. This ad-hoc hypothesis introduced into young-Earth creationism makes it non falsifiable, because it says that the technology used to measure the time of creation is false and no other accepted technology is proposed to replace it. Popper says that it's fine to modify a theory by the introduction of an auxiliary hypothesis as long as it increases falsifiability. Otherwise, it's an unwanted ad-hoc hypothesis. The new theory must at the least remains falsifiable, which is not the case here. One can also present the Omphalos hypothesis as an auxiliary hypothesis that is introduced into the accepted theory. In this view also, it does not increase falsifiability, because no additional observations are predicted. In both views, the ad-hoc hypothesis, seen by itself, is not falsifiable because there is no way to measure the (hidden) time of creation that is proposed by this hypothesis. This is discussed in details by Dienes in the case of a variation on the Omphalos hypothesis, which, in addition, specifies that God made the creation in this way to test our faith.[27]

Historicism

Theories of history or politics that allegedly predict future events have a logical form that renders them neither falsifiable nor verifiable. They claim that for every historically significant event, there exists an historical or economic law that determines the way in which events proceeded. Failure to identify the law does not mean that it does not exist, yet an event that satisfies the law does not prove the general case. Evaluation of such claims is at best difficult. On this basis, Popper "fundamentally criticized historicism in the sense of any preordained prediction of history"[28] and argued that neither Marxism nor psychoanalysis was science,[28] although both made such claims. Again, this does not mean that any of these types of theories is necessarily incorrect. Popper considered falsifiability a test of whether theories are scientific, not of whether propositions that they contain or support are true.

Mathematics

Like all formal sciences, mathematics is not concerned with the validity of theories based on observations in the empirical world, but rather, mathematics is occupied with the theoretical, abstract study of such topics as quantity, structure, space and change. Methods of the mathematical sciences are, however, applied in constructing and testing scientific models dealing with observable reality. Albert Einstein wrote, "One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts."[29]

Notes

The observations used to contradict and thus falsify laws cannot be all possible, because the criterion must be able to accept true laws. Besides this obvious problem, Popper mentions more important problems created when we do not distinguish between falsifiability in the logical sense and falsifiability as understood in the common language (see Popper 1983, Introduction, 1982): "Although the first sense refers to the logical possibility of a falsification in principle, the second sense refers to a conclusive practical experimental proof of falsity. But anything like conclusive proof to settle an empirical question does not exist. An entire literature rests on the failure to observe this distinction." For a discussion related to this lack of distinction, see Rosende 2009, p. 142.
"All swans are white" is often chosen as an example of a falsifiable statement, because for some 1500 years, the black swan existed in the European imagination as a metaphor for that which could not exist. Had the presumption concerning black swans in this metaphor be right, the statement would still have been falsifiable.
The valid inference rule modus tollens says that, given the implication p ⟶ q, if the antecedent p is affirmed, we can infer the consequent q. The fallacy "affirming the consequent" flips the antecedent with the consequent and says that, given the same implication, if the consequent q is affirmed, we can infer the antecedent p. This fallacy supports an argument from the observed q="here is a white swan" to p'="all swans are white", because, introducing p="all swans are white and here is a swan", we have p ⟶ q and p ⟶ p' and thus, if the consequent q is affirmed, we can (fallaciously) infer p and then legitimately infer p'.
We cannot really falsify "all swans are white," because one can always allude to initial conditions that explain the contradicting observation. In this case, perhaps the observer confused a black raven for a swan. This is one of many issues with dogmatic falsificationism.
Lakatos refers to Popper 1959 when he credits Popper for sophisticated falsificationism. See Lakatos 1978, pp. 33 and 35.
Popper 1983, Introduction, IV: "This may be the place to mention, and to refute, the legend that Thomas S. Kuhn, in his capacity as a historian of science, is the one who has shown that my views on science (sometimes, but not by me, called 'falsificationismism') can be refuted by the facts; that is to say, by the history of science."
Popper 1963, p. 26: "The proper answer to my question 'How can we hope to detect and eliminate error?' is, I believe, 'By criticizing the theories or guesses of others and—if we can train ourselves to do so—by criticizing our own theories or guesses.' (The latter point is highly desirable, but not indispensable; for if we fail to criticize our own theories, there may be others to do it for us.) This answer sums up a position which I propose to call 'critical rationalism'."
Popper 1963, p. 111: "Against the view here developed one might be tempted to object (following Duhem 28 ) that in every test it is not only the theory under investigation which is involved, but also the whole system of our theories and assumptions—in fact, more or less the whole of our knowledge—so that we can never be certain which of all these assumptions is refuted. But this criticism overlooks the fact that if we take each of the two theories (between which the crucial experiment is to decide) together with all this background knowledge, as indeed we must, then we decide between two systems which differ only over the two theories which are at stake. It further overlooks the fact that we do not assert the refutation of the theory as such, but of the theory together with that background knowledge; parts of which, if other crucial experiments can be designed, may indeed one day be rejected as responsible for the failure. (Thus we may even characterize a theory under investigation as that part of a vast system for which we have, if vaguely, an alternative in mind, and for which we try to design crucial tests.)"
Popper 1959, p. 19: "It might be said that even if the asymmetry [between universal and existential statements] is admitted, it is still impossible, for various reasons, that any theoretical system should ever be conclusively falsified. For it is always possible to find some way of evading falsification, for example by introducing ad hoc an auxiliary hypothesis, or by changing ad hoc a definition. It is even possible without logical inconsistency to adopt the position of simply refusing to acknowledge any falsifying experience whatsoever. Admittedly, scientists do not usually proceed in this way, but logically such procedure is possible; and this fact, it might be claimed, makes the logical value of my proposed criterion of demarcation dubious, to say the least."
Lakatos explains that, if the ceteris paribus clause is false, both Newton theory and Freud theory can avoid a logical falsification, but he fails to say that for many falsifiers of Newton theory, the clause is true under normal assumptions and thus is not really required as a separate clause. Popper was concerned that Lakatos meant that Newton theory could be put in the same category as Freud theory and wrote a response of 5 pages in Popper 1974, pp. 1004–1009 to clarify this issue. See also Popper 2009, Introduction, 1978: "[S]ome of my former students ... believe that any putative falsification of Newtonian theory may be turned into a victory by assuming the existence of an unknown (and perhaps invisible) mass. However, this is simply a physical (or mathematical) error. First, there are many motions that in principle are observable but that cannot be explained by any such auxiliary hypothesis (for instance, a sudden reversal of motions)."
Popper 1983, p. XXII: "We must distinguish two meanings of the expressions falsifiable and falsifiability:
"1) Falsifiable as a logical-technical term, in the sense of the demarcation criterion of falsifiability. This purely logical concept — falsifiable in principle, one might say — rests on a logical relation between the theory in question and the class of basic statements (or the potential falsifiers described by them).
"2) Falsifiable in the sense that the theory in question can definitively or conclusively or demonstrably be falsified ("demonstrably falsifiable").
"I have always stressed that even a theory which is obviously falsifiable in the first sense is never falsifiable in this second sense. (For this reason I have used the expression falsifiable as a rule only in the first, technical sense. In the second sense, I have as a rule spoken not of falsifiability but rather of falsification and of its problems)"
Lakatos add two other decisions. One of them is needed to accept statistical statements as falsifiable. The other allows even more falsifiable theories.
Popper 1959, p. 94: "Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or 'given' base; and if we stop driving the piles deeper, it is not because we have reached firm ground. We simply stop when we are satisfied that the piles are firm enough to carry the structure, at least for the time being."
Popper 1959, p. 91: "It may now be possible for us to answer the question: How and why do we accept one theory in preference to others? The preference is certainly not due to anything like a experiential justification of the statements composing the theory; it is not due to a logical reduction of the theory to experience. We choose the theory which best holds its own in competition with other theories; the one which, by natural selection, proves itself the fittest to survive. This will be the one which not only has hitherto stood up to the severest tests, but the one which is also testable in the most rigorous way. A theory is a tool which we test by applying it, and which we judge as to its fitness by the results of its applications."
Lakatos explains that Popper is not the sophisticated falsificationist that he describes, but, of course, not the naive falsificationist either (see Lakatos 1978): "In an earlier paper,' I distinguished three Poppers: Popper0, Popper1, and Popper2. Popper0 is the dogmatic falsificationist ... Popper1 is the naive falsificationist, Popper2 the sophisticated falsificationist. ... The real Popper has never explained in detail the appeal procedure by which some 'accepted basic statements', may be eliminated. Thus the real Popper consists of Popper1 together with some elements of Popper2."
Thornton 2016, sec. 3: "Popper has always drawn a clear distinction between the logic of falsifiability and its applied methodology. The logic of his theory is utterly simple: if a single ferrous metal is unaffected by a magnetic field it cannot be the case that all ferrous metals are affected by magnetic fields. Logically speaking, a scientific law is conclusively falsifiable although it is not conclusively verifiable. Methodologically, however, the situation is much more complex: no observation is free from the possibility of error—consequently we may question whether our experimental result was what it appeared to be."
Popper clearly distinguishes between the methodological rules and the rules of pure logic (see Popper 1959, p. 32): "Methodological rules are here regarded as conventions. They might be described as the rules of the game of empirical science. They differ from the rules of pure logic..."
Popper 1959, p. 27: "The theory of method, in so far as it goes beyond the purely logical analysis of the relations between scientific statements, is concerned with the choice of methods—with decisions about the way in which scientific statements are to be dealt with."
Zahar wrote a brief summary of Lakatos's position regarding Popper's philosophy. He explains (see Zahar 1983, p. 149): "The important question of the possibility of a genuine logic of [scientific] discovery" is the main divergence between Lakatos and Popper. About Popper's view, Zahar wrote (see Zahar 1983, p. 169): "To repeat: Popper offers a Darwinian account of the progress of knowledge. Progress is supposed to result negatively from the elimination by natural selection of defective alternatives. ... There is no genuine logic of discovery, only a psychology of invention juxtaposed to a methodology which appraises fully fledged theories."
In Lakatos terminology, the term "falsified" has a different meaning for a naive falsificationist than for a sophisticated falsificationist. Putting aside this confusing terminological aspect, the key point is that Lakatos wanted a formal logical procedure to determine which theories we must keep (see Lakatos 1978, p. 32): "For the naive falsificationist a theory is falsified by a ('fortified') 'observational' statement which conflicts with it (or which he decides to interpret as conflicting with it). For the sophisticated falsificationist a scientific theory T is falsified if and only if another theory T' has been proposed with the following characteristics: ( 1 ) T' has excess empirical content over T: that is, it predicts novel facts, that is, facts improbable in the light of, or even forbidden, by (2) T' explains the previous success of T, that is, all the unrefuted content of T is included (within the limits of observational error) in the content of T'; and (3) some of the excess content of T' is corroborated."
In his critique of Popper (see Kuhn 1965, p. 15), Kuhn says that the methodological rules are not sufficient to provide a logic of discovery: "... rules or conventions like the following: 'Once a hypothesis has been proposed and tested, and has proved its mettle, it may not be allowed to drop out without 'good reason'. A 'good reason' may be, for instance: replacement of the hypothesis by another which is better testable; or the falsification of one of the consequences of the hypothesis.'
Rules like these, and with them the entire logical enterprise described above, are no longer simply syntactic in their import. They require that both the epistemological investigator and the research scientist be able to relate sentences derived from a theory not to other sentences but to actual observations and experiments. This is the context in which Sir Karl's term 'falsification' must function, and Sir Karl is entirely silent about how it can do so."
Popper gives an example of a methodological rule that uses corroborations (see Popper 1959, p. 32): "Once a hypothesis has been proposed and tested, and has proved its mettle, it may not be allowed to drop out without 'good reason'. A 'good reason' may be, for instance: replacement of the hypothesis by another which is better testable; or the falsification of one of the consequences of the hypothesis."
Popper 1959, section 23, 1st paragraph: "The requirement of falsifiability which was a little vague to start with has now been split into two parts. The first, the methodological postulate (cf. section 20), can hardly be made quite precise. The second, the logical criterion, is quite definite as soon as it is clear which statements are to be called 'basic'."
Popper 1959, p. 9: "According to the view that will be put forward here, the method of critically testing theories, and selecting them according to the results of tests, always proceeds on the following lines. From a new idea, put up tentatively, and not yet justified in any way—an anticipation, a hypothesis, a theoretical system, or what you will—conclusions are drawn by means of logical deduction. These conclusions are then compared with one another and with other relevant statements, so as to find what logical relations (such as equivalence, derivability, compatiblity, or incompatibility) exist between them."
Popper 1983, Introduction, V: "The hope further to strengthen this theory of the aims of science by the definition of verisimilitude in terms of truth and of content was, unfortunately, vain. But the widely held view that scrapping this definition weakens my theory is completely baseless."
Popper 1983, chap. 1, sec. 3: "It seems that almost everybody believes in induction; believes, that is, that we learn by the repetition of observations. Even Hume, in spite of his great discovery that a natural law can neither be established nor made 'probable' by induction, continued to believe firmly that animals and men do learn through repetition: through repeated observations as well as through the formation of habits, or the strengthening of habits, by repetition. And he upheld the theory that induction, though rationally indefensible and resulting in nothing better than unreasoned belief, was nevertheless reliable in the main— more reliable and useful at any rate than reason and the processes of reasoning; and that 'experience' was thus the unreasoned result of a (more or less passive) accumulation of observations. As against all this, I happen to believe that in fact we never draw inductive inferences, or make use of what are now called 'inductive procedures'. Rather, we always discover regularities by the essentially different method of trial and error."
Popper 1963, p. 35: "As for Adler, I was much impressed by a personal experience. Once, in 1919, I reported to him a case which to me did not seem particularly Adlerian, but which he found no difficulty in analysing in terms of his theory of inferiority feelings, although he had not even seen the child. Slightly shocked, I asked him how he could be so sure. 'Because of my thousandfold experience,' he replied; whereupon I could not help saying: 'And with this new case, I suppose, your experience has become thousand-and-one-fold.'"
In Popper's description of the scientific procedure of testing, there is no mention of factual observations except in those tests that compare the theory with factual observations, but in these tests too the procedure is mostly logical and involves observations that are only logical constructions (Popper 1959, pp. 9–10): "We may if we like distinguish four different lines along which the testing of a theory could be carried out. First there is the logical comparison of the conclusions among themselves, by which the internal consistency of the system is tested. Secondly, there is the investigation of the logical form of the theory, with the object of determining whether it has the character of an empirical or scientific theory, or whether it is, for example, tautological. Thirdly, there is the comparison with other theories, chiefly with the aim of determining whether the theory would constitute a scientific advance should it survive our various tests. And finally, there is the testing of the theory by way of empirical applications of the conclusions which can be derived from it. ... Here too the procedure of testing turns out to be deductive. With the help of other statements, previously accepted, certain singular statements—which we may call 'predictions'—are deduced from the theory; especially predictions that are easily testable or applicable. From among these statements, those are selected which are not derivable from the current theory, and more especially those which the current theory contradicts."
Popper 1974, p. 1005: " ... would contradict Newton's theory. This theory would equally be contradicted if the apples from one of my, or Newton's, apple trees were to rise from the ground (without there being a whirling about), and begin to dance round the branches of the apple tree from which they had fallen."
If the criteria to identify an angel was simply to observe large wings, then "this angel does not have large wings" would be a logical contradiction and thus not a basic statement anyway.
Popper 1959, section 7, page 21: "If falsifiability is to be at all applicable as a criterion of demarcation, then singular statements must be available which can serve as premisses in falsifying inferences. Our criterion therefore appears only to shift the problem—to lead us back from the question of the empirical character of theories to the question of the empirical character of singular statements.
"Yet even so, something has been gained. For in the practice of scientific research, demarcation is sometimes of immediate urgency in connection with theoretical systems, whereas in connection with singular statements, doubt as to their empirical character rarely arises. It is true that errors of observation occur and that they give rise to false singular statements, but the scientist scarcely ever has occasion to describe a singular statement as non-empirical or metaphysical."
Popper 1963, p. 387: "Before using the terms 'basic' and 'basic statement', I made use of the term 'empirical basis', meaning by it the class of all those statements which may function as tests of empirical theories (that is, as potential falsifiers). In introducing the term 'empirical basis' my intention was, partly, to give an ironical emphasis to my thesis that the empirical basis of our theories is far from firm; that it should be compared to a swamp rather than to solid ground."
Kuhn 1974, p. 802: "I suggest then that Sir Karl has characterized the entire scientific enterprise in terms that apply only to its occasional revolutionary parts. His emphasis is natural and common: the exploits of a Copernicus or Einstein make better reading than those of a Brahe or Lorentz; Sir Karl would not be the first if he mistook what I call normal science for an intrinsically uninteresting enterprise. Nevertheless, neither science nor the development of knowledge is likely to be understood if research is viewed exclusively through the revolutions it occasionally produces."
Watkins 1970, p. 28: "Thus we have the following clash: the condition which Kuhn regards as the normal and proper condition of science is a condition which, if it actually obtained, Popper would regard as unscientific, a state of affairs in which critical science had contracted into defensive metaphysics. Popper has suggested that the motto of science should be: Revolution in permanence! For Kuhn, it seems, a more appropriate maxim would be: Not nostrums but normalcy!"
Popper 1994, pp. 155–156: "It is my view that the methods of the natural as well as the social sciences can be best understood if we admit that science always begins and ends with problems. The progress of science lies, essentially, in the evolution of its problems. And it can be gauged by the increasing refinement, wealth, fertility, and depth of its problems. ... The growth of knowledge always consists in correcting earlier knowledge. Historically, science begins with pre-scientific knowledge, with pre-scientific myths and pre-scientific expectations. And these, in turn, have no 'beginnings'."
Surveys were mailed to all active U.S. district court judges in November 1998 (N = 619). 303 usable surveys were obtained for a response rate of 51%.
The Daubert case and subsequent cases that used it as a reference, including General Electric Co. v. Joiner and Kumho Tire Co. v. Carmichael, resulted in an amendment of the Federal Rules of Evidence (see Rules of Evidence 2017, p. 15, Rule 702 and Rule 702 Notes 2011). The Kumho Tire Co. v. Carmichael case and other cases considered the original Daubert factors, but the amended rule, rule 702, even though it is often referred to as the Daubert standard, does not include the original Daubert factors or mention falsifiability or testability and neither does the majority opinion delivered by William Rehnquist in the General Electric Co. v. Joiner case.
Not to be confused with David Kaye (law professor), United Nations special rapporteur. David H. Kaye is distinguished professor of law at Penn State Law.
Kaye 2005, p. 2: "... several courts have treated the abstract possibility of falsification as sufficient to satisfy this aspect of the screening of scientific evidence. This essay challenges these views. It first explains the distinct meanings of falsification and falsifiability. It then argues that while the Court did not embrace the views of any specific philosopher of science, inquiring into the existence of meaningful attempts at falsification is an appropriate and crucial consideration in admissibility determinations. Consequently, it concludes that recent opinions substituting mere falsifiability for actual empirical testing are misconstruing and misapplying Daubert."
Thornton 2016: "For Marxism, Popper believed, had been initially scientific, in that Marx had postulated a theory which was genuinely predictive. However, when these predictions were not in fact borne out, the theory was saved from falsification by the addition of ad hoc hypotheses which made it compatible with the facts. By this means, Popper asserted, a theory which was initially genuinely scientific degenerated into pseudo-scientific dogma."

Abbreviated references

Popper 1989, pp. 82–85.
Grayling 2019, p. 397.
Lakatos 1978, pp. 12–30.
Fine 2019.
Popper 1963.
Uebel 2019.
Creath 2017.
Thornton 2016, sec. 4.
Kuhn 1996.
Martin 2017.
Feyerabend 1993.
Broad 1979.
Sokal & Bricmont 1998.
Miller 2000.
McLean v. Arkansas 1982.
Daubert 1993.
Heath 2015.
Mises 1998, p. 11.
Theobald 2006.
Ridley 2003.
Wallis 2005.
Dawkins 1995.
Dawkins 1986.
Popper 1982b.
Popper 1976.
Popper 1978.
Dienes 2008, pp. 18–19.
Burton 2000, p. 12–13.
Einstein 2010.

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Karl Popper
Philosophy	Bold hypothesis Critical rationalism Falsifiability Growth of knowledge Open society Popper's experiment Popper's three worlds Verisimilitude
Works	The Logic of Scientific Discovery (1934) The Poverty of Historicism (1936) The Open Society and Its Enemies (1945) Conjectures and Refutations (1963) Unended Quest (1976) The Myth of the Framework (1994)